1. Brief Review of Superbunches for Hadron Colliders
Frank Zimmermann, Factories’03
History & Motivation
Tune Shift
Optimum Luminosity

2. Collider Commissioning year Energy [GeV] Peak Luminosity
The CERN ISR - the first hadron collider - collided coasting (unbunched) proton beams with currents up to 50 A and reached
a peak luminosity of 2.2x1032cm-2s-1. This has not yet been
achieved by any other hadron collider.
Collider
Commissioning year
Energy [GeV]
Peak Luminosity
[1032 cm-2s-1]
ISR
1970 31
1.4
SPPS
1980
316
0.06
Tevatron
1987
980
0.4
RHIC
2000
100
0.02 (polarized)
LHC
2007
7000
LHC-II?
2017?
>7000?
>1000?

3. ISR-style quasi-coasting beams recently identified as key ingredient for future highest-energy high-luminosity proton colliders [e.g., Ken Takayama et al., ‘Superbunch Hadron Colliders,’ Phys. Rev. Lett 88, (2002).]
In particular, a possible upgrade of the Large Hadron Collider (LHC) [2] can be considered, by operating not exactly with coasting beams, but with long super-bunches, which are confined, e.g., by a barrier bucket rf system. [F. Ruggiero (ed.), et al., ‘LHC Luminosity and Energy Upgrade: A Feasibility Study,’ CERN LHC Project Report 626 (2002).]

4. LHC: nominal, ultimate, and possible upgrades
#bunches
2808 1
rms bunch length [cm]
7.6
7.6, 4.2
7500
rms energy spread [10-4]
1.1
1.1, 3.7
5.8
beta at IP [m]
0.5
0.25
crossing angle[mrad]
300
315
485
1000
beam current [A]
0.56
0.86
1.3,1.3
1.0
luminosity [1034 cm-2 s-1]
2.3
7.3, 9.7
9.0

5. main advantages:
cancellation between head-on and ‘long-range’ components of the beam-beam tune shift, which is realized by colliding the beams at two interaction points with alternating planes of crossing
absence of PACMAN bunches at the end of a bunch train
no beam-induced multipacting and electron-cloud build up

6. cancellation between head-on and ‘long-range’ components
of the beam-beam tune shift
PRSTAB 5, (2002)

7. x-y crossing or 45/135 degree crossing

8. (1) luminosity of a conventional hadron collider operating with round bunched Gaussian beams can be increased in proportion to the bunch current, while keeping a constant beam-beam tune shift, by enlarging the product of bunch length and crossing angle
(2) if one chooses a uniform profile instead of a Gaussian, an
additional factor sqrt(2) is gained
[F. Ruggiero, F. Zimmermann, ‘Luminosity Optimization Near the Beam-Beam Limit by Increasing Bunch Length or Crossing Angle,’ PRSTAB 5, (2002)]

9. total tune shift for flat bunches colliding at 2 IPs
with alternating crossings
total tune shift for Gaussian bunches

10. further simplifying assumptions:
Gaussian bunches
(i) q<<1 rad
(ii) s* <<sz<<b
(iii) large Piwinski parameter qsz /(2s*)>>1
Long flat superbunches
(ii) q>sqrt(e/(gb*))
(iii) lflat>10 s*/q

11. Gaussian bunches
proportional to qsz!

12. flat superbunches
proportional to ql!

13. F. Ruggiero, F. Zimmermann, G. Rumolo, Y. Papaphilippou,
“Beam Dynamics Studies for Uniform (Hollow) Bunches or Super-bunches in the LHC : Beam-beam effects, Electron Cloud, Longitudinal Dynamics, and Intrabeam Scattering”, RPIA2002
“Beam-Beam Interaction, Electron Cloud and Intrabeam Scattering for Proton Super-bunches”, PAC2003

14. LHC, L0=2.3x1034 cm-2 s-1, q0=300 mrad

15. Conclusion:
Operating with large Piwinski parameter
or preferably with flat superbunches,
LHC luminosity can be increased about
10 times to 1035 cm-2 s-1 for the same total
tune shift and beam current
Problems with PACMAN bunches and
electron cloud are solved simultaneously